In an interview with state broadcaster TRT, Davutoglu said Erdogan would not be involved in coalition negotiations after the AKP lost its parliamentary majority in a weekend election, and that he would only intervene in the event of a crisis.
Sunday's election ended more than a decade of single-party rule in the NATO member and EU candidate nation, dealing a blow to Erdogan's ambitions for a powerful U.S.-style presidency and plunging it into political uncertainty not seen since the 1990s.
"President Erdogan is not part of coalition negotiations but will step in to help overcome deadlocks," Davutoglu said in the hour-long interview.
"If everybody carries out their duties and responsibilities within the constitutional limits, a culture of reconciliation will emerge," he said, in an apparent warning to Erdogan.
Opposition parties have accused Erdogan, who founded the AKP more than a decade ago and remains its dominant figure, of continuing to meddle in its affairs despite a constitutional ban on him engaging in party politics as head of state.
In contrast to his usual dominance of the air waves, Erdogan has yet to make any public comments since the election, apart from a brief statement from his office urging a period of reflection by all political parties.
Daily Sabah, a newspaper close to Erdogan, has said he has three red lines for any coalition: the continuation of a peace process with Kurdish militants, respect for his role as president, and the continuation of the fight against the "parallel state" - the network of U.S.-based cleric Fethullah Gulen, whom he accuses of plotting against him.
"Nobody can declare red lines in the name of the AK Party," Davutoglu said in the interview with TRT.
Forced to find a coalition partner for the first time in its history or risk an unstable minority government, the conservative, Islamist-rooted AKP's top brass held a third day of meetings on Wednesday to consider their options.
Should the political parties be unable to agree a working coalition within 45 days, Erdogan has the right to call a snap election, but AKP officials say that is not their preferred route.
Davutoglu also said the AKP would pursue a peace process with Kurdish militants for as long as possible, whatever the outcome of coalition negotiations. One of its possible junior partners, the right-wing Nationalist Movement Party (MHP), has long been opposed to the Kurdish peace process.